Many complex disease syndromes consist of a large number of highly related, rather than independent, clinical phenotypes. Differences between these syndromes involve the complex interplay of a large number of genomic variations that perturb the function of disease-related genes in the context of a regulatory network, rather than individually. Thus unraveling the causal genetic variations and understanding the mechanisms of consequent cell and tissue transformation requires an analysis that jointly considers the epistatic, pleiotropic, and plastic interactions of elements and modules within and between the genome (G), transcriptome (T), and phenome (P). Most conventional methods focus on associations between every individual marker genotype and every single phenotype; they have limited statistical power and overlook the complex omit structures. We propose a systematic attempt on methodological development for the largely unexplored but practically important problem of structured associations between the -omes. Rather than testing each SNP separately for association and then applying a correction by multiple hypothesis test, a structured association analysis identifies associations between groups of entities each with its own sophisticated structure that can not be ignored, such as blocks of SNPs with high LD, modules of genes in the same pathway, and clusters of phenotypes belong to a system of clinical descriptors of a disease. We will develop a mathematically rigorous and computationally efficient machine learning platform and software to address the methodological challenges involved with unraveling the interplay between disease-relevant elements in the G, T, and P omes. Our technical innovations include novel statistical models and algorithms for haplotype inference, recombination hotspot detection, gene network and phenotype network inference, admixture association mapping, and most importantly, a family of new structured regression techniques such as the graph-regularized regression, graph- guided fused lasso and extensions, that perform functional approximations to the association functions among structural elements in the G, T, and P omes, and have provable guarantee on consistency and sparsistency. We envisage our proposed research will open a new paradigm for association studies of complex diseases, which facilitates: 1) Intra- and inter-omic integration of data for association mapping and disease gene/pathway discovery, 2) Thorough explorations of the internal structures within different omic data, so that cryptic associations that are not possibly detectable in unstructured analysis due to their weak statistical power can be now inferred. 3) Joint statistical inference of mechanisms and pathways of how variations in DNA lead to variations in complex traits flows through molecular networks, and inference of condition-specific state of gene function in the molecular networks, and 4) Development of faster and automated computational algorithm with greater scalability and robustness to large-scale inter-omic analysis, and more convenient software package and user interface. All the software tools will be made available for free to the public.